Abstract
If {X α } is any family of spaces, then βX α βX α ) is a compactification of X α . In Example 1.67 we observed that in the case of ℝ x ℝ. βℝ x βℝ is not the Stone-Čech compactification of ℝ x ℝ. The present chapter will be largely devoted to determining when it will be true that (βX α ), is β X α ), i. e. when X α will be C*-embedded in (βX α ). I, Glicksberg showed in 1959 that for infinite spaces, this will be the case exactly when the product α is pseudocompact.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1974 Springer-Verlag Berlin Heidelberg New York
About this chapter
Cite this chapter
Walker, R.C. (1974). Product Theorems. In: Walker, R.C. (eds) The Stone-Čech Compactification. Ergebnisse der Mathematik und ihrer Grenzgebiete, vol 83. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-61935-9_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-61935-9_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-61937-3
Online ISBN: 978-3-642-61935-9
eBook Packages: Springer Book Archive